Nicolas Garcia Trillos

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Featured Co-authors

Matthias Hein
83 publications
Youssef Marzouk
38 publications
Xavier Bresson
30 publications
Jeff Calder
28 publications
Thomas Laurent
23 publications
Daniel Sanz-Alonso
22 publications
James M. Murphy
20 publications
José A. Carrillo
19 publications
Leon Bungert
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Dejan Slepčev
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Matthew Thorpe
15 publications

research

∙ 07/07/2023

Fermat Distances: Metric Approximation, Spectral Convergence, and Clustering Algorithms

We analyze the convergence properties of Fermat distances, a family of d...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 07/05/2023

Continuum Limits of Ollivier's Ricci Curvature on data clouds: pointwise consistency and global lower bounds

Let ℳ⊆ℝ^d denote a low-dimensional manifold and let 𝒳= { x_1, …, x_n } b...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 05/30/2023

It begins with a boundary: A geometric view on probabilistically robust learning

Although deep neural networks have achieved super-human performance on m...

0 Leon Bungert, et al. ∙

research

∙ 05/04/2023

FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimization

Federated learning is an important framework in modern machine learning ...

0 José A. Carrillo, et al. ∙

research

∙ 04/28/2023

On the existence of solutions to adversarial training in multiclass classification

We study three models of the problem of adversarial training in multicla...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 01/09/2023

On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it

We propose iterative algorithms to solve adversarial problems in a varie...

0 Camilo Garcia Trillos, et al. ∙

research

∙ 10/13/2022

Wasserstein Barycenter-based Model Fusion and Linear Mode Connectivity of Neural Networks

Based on the concepts of Wasserstein barycenter (WB) and Gromov-Wasserst...

0 Aditya Kumar Akash, et al. ∙

research

∙ 09/29/2022

Nonconvex Matrix Factorization is Geodesically Convex: Global Landscape Analysis for Fixed-rank Matrix Optimization From a Riemannian Perspective

We study a general matrix optimization problem with a fixed-rank positiv...

0 Yuetian Luo, et al. ∙

research

∙ 09/06/2022

Rates of Convergence for Regression with the Graph Poly-Laplacian

In the (special) smoothing spline problem one considers a variational pr...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 07/03/2022

Mathematical Foundations of Graph-Based Bayesian Semi-Supervised Learning

In recent decades, science and engineering have been revolutionized by a...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 04/27/2022

The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classification

We study a family of adversarial multiclass classification problems and ...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 11/26/2021

The Geometry of Adversarial Training in Binary Classification

We establish an equivalence between a family of adversarial training pro...

0 Leon Bungert, et al. ∙

research

∙ 09/13/2021

On the regularized risk of distributionally robust learning over deep neural networks

In this paper we explore the relation between distributionally robust le...

0 Camilo Garcia Trillos, et al. ∙

research

∙ 08/18/2021

Clustering dynamics on graphs: from spectral clustering to mean shift through Fokker-Planck interpolation

In this work we build a unifying framework to interpolate between densit...

5 Katy Craig, et al. ∙

research

∙ 07/28/2021

Large sample spectral analysis of graph-based multi-manifold clustering

In this work we study statistical properties of graph-based algorithms f...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 11/21/2020

Adversarial Classification: Necessary conditions and geometric flows

We study a version of adversarial classification where an adversary is e...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 07/13/2020

Lipschitz regularity of graph Laplacians on random data clouds

In this paper we study Lipschitz regularity of elliptic PDEs on geometri...

0 Jeff Calder, et al. ∙

research

∙ 06/26/2020

Semi-discrete optimization through semi-discrete optimal transport: a framework for neural architecture search

In this paper we introduce a theoretical framework for semi-discrete opt...

8 Nicolas Garcia Trillos, et al. ∙

research

∙ 06/26/2020

Traditional and accelerated gradient descent for neural architecture search

In this paper, we introduce two algorithms for neural architecture searc...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 04/20/2020

From graph cuts to isoperimetric inequalities: Convergence rates of Cheeger cuts on data clouds

In this work we study statistical properties of graph-based clustering a...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 03/18/2020

Data-Driven Forward Discretizations for Bayesian Inversion

This paper suggests a framework for the learning of discretizations of e...

0 Daniele Bigoni, et al. ∙

research

∙ 10/29/2019

Improved spectral convergence rates for graph Laplacians on epsilon-graphs and k-NN graphs

In this paper we improve the spectral convergence rates for graph-based ...

0 Jeff Calder, et al. ∙

research

∙ 04/06/2019

Local Regularization of Noisy Point Clouds: Improved Global Geometric Estimates and Data Analysis

Several data analysis techniques employ similarity relationships between...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 01/30/2019

Geometric structure of graph Laplacian embeddings

We analyze the spectral clustering procedure for identifying coarse stru...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 01/29/2019

A maximum principle argument for the uniform convergence of graph Laplacian regressors

We study asymptotic consistency guarantees for a non-parametric regressi...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 01/29/2019

Variational Characterizations of Local Entropy and Heat Regularization in Deep Learning

The aim of this paper is to provide new theoretical and computational un...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 08/09/2018

Spatial extreme values: variational techniques and stochastic integrals

This work employs variational techniques to revisit and expand the const...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 01/30/2018

Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operator

We study the convergence of the graph Laplacian of a random geometric gr...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 10/20/2017

On the Consistency of Graph-based Bayesian Learning and the Scalability of Sampling Algorithms

A popular approach to semi-supervised learning proceeds by endowing the ...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 06/22/2017

Continuum Limit of Posteriors in Graph Bayesian Inverse Problems

We consider the problem of recovering a function input of a differential...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 02/11/2017

Gromov-Hausdorff limit of Wasserstein spaces on point clouds

We consider a point cloud X_n := { x_1, ..., x_n } uniformly distributed...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 07/03/2016

Variational limits of k-NN graph based functionals on data clouds

We consider i.i.d. samples x_1, ..., x_n from a measure ν with density s...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 07/01/2016

A new analytical approach to consistency and overfitting in regularized empirical risk minimization

This work considers the problem of binary classification: given training...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 08/08/2015

A variational approach to the consistency of spectral clustering

This paper establishes the consistency of spectral approaches to data cl...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 11/24/2014

Consistency of Cheeger and Ratio Graph Cuts

This paper establishes the consistency of a family of graph-cut-based al...

0 Nicolas Garcia Trillos, et al. ∙

research

∙ 03/25/2014

Continuum limit of total variation on point clouds

We consider point clouds obtained as random samples of a measure on a Eu...

0 Nicolas Garcia Trillos, et al. ∙

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